The present invention relates to a method for characterizing samples having fluorescent particles and applications of said method.
The utilization of fluorescence has evolved rapidly during the past decades because it offers high sensitivity in various scientific applications. New developments in instrumentation, data analysis, probes and employment have resulted in enhanced popularity for a technique that relies on a phenomenon discovered nearly 150 years ago (Stokes, Phil. Trans. R. Soc. Lond. 142, 463-562, 1852). In a number of applications in physical chemistry, biology and medicine, fluorescence is used as a sensitive means of detecting chemical binding reactions in dilute solutions. Drug screening and pharmaceutical assay development are examples of fields of applications of this kind.
In addition to classical methods based on detecting changes in macroscopic fluorescence characteristics such as overall intensity or anisotropy, a number of different fluctuation methods have been developed during the last decades distinguishing species on ground of properties characteristic to single molecules. One of the most elaborated fluorescence techniques with single molecule sensitivity is fluorescence correlation spectroscopy (FCS) that can resolve different species first of all on the basis of different translational diffusion coefficient (Magde et al., Phys. Rev. Lett. 29, 104-708, 1972; Elson et al., Biopolymers 13, 1-27, 1974; Rigler et al., Eur. Biophys. J 22, 169-175, 1993). Recently, this fluorescence fluctuation method found its counterpart in fluorescence intensity distribution analysis (FIDA) that discriminates different fluorescent species according to their specific brightness (Kask et al., Proc. Natl. Acad. Sci. USA 96, 13756-13761, 1999). The term xe2x80x9cspecific brightnessxe2x80x9d generally denotes the mean count rate of the detector from light emitted by a particle of given species situated in a certain point in the sample, conventionally in the point where the value of the brightness profile function is unity.
Aside methods like FCS and FIDA which distinguish species on the ground of a single specific physical property, two-dimensional methods have been developed, utilizing two detectors monitoring different polarization components or emission bands of fluorescence. In particular, fluorescence cross-correlation analysis and two-dimensional fluorescence intensity distribution analysis (2D-FIDA) are methods recognizing species on the ground of two types of specific brightness (Kask et al., Biophys. J. 55, 213-220, 1989; Schwille et al., Biophys J. 72, 1878-1886, 1997; Kask et al. Biophys. J. 78, 2000).
While FCS, FIDA and the mentioned two-dimensional methods are statistical methods of fluctuation spectroscopy, there is also another broad field of research having the goal to identify individual molecules. Many applications make use of the fluorescence lifetime as an intrinsic molecular property that is sensitive to any changes of the molecule""s direct environment. However, different from the above mentioned fluctuation methods, fluorescence lifetime analysis (FLA) is basically a macroscopic technique that allows the discrimination of different fluorescence decay times without the need for molecular number fluctuations in the monitored sample volume. Therefore, fluorescence lifetime measurements are usually performed in cuvettes at high sample concentrations. However, the disadvantage of this implementation is that the experimentally collected excitation to detection delay time histogram has contributions from different species which are difficult to be resolved. In addition, FLA has only a low robustnessxe2x80x94slightly wrong assumptions yield very wrong results.
On the contrary, lifetime experiments have also been applied to extremely low mean particle numbers. This approach, being opposed to conventional FLA, was introduced as burst integrated fluorescence lifetime analysis (BIFL) (Keller et al., Applied Spectroscopy 50, 12A-32A, 1996). BIFL searches for fluorescence bursts from single molecules above a certain threshold intensity. Its disadvantage is that it can only be applied at very low concentrations of significantly less than one particle per measurement volume and therefore relatively long data collection time is needed.
In fluorescence lifetime experiments, if performed in the time domain with time correlated single photon counting (TCSFC), the excitation to detection delay time, t, of single photons is recorded and collected in a histogram. To extract the fluorescence lifetime a theoretical distribution P(t) is fitted against these experimental data. Usually P(t) is described by a single- or multi-exponential decay function that is convoluted with the respective instrument response function (IRF). Whereas this kind of analysis allows to characterize constituents of the sample according to their individual lifetimes, xcfx84, it does not allow the determination of their concentrations, c, and specific brightness, q, but only the products, qc.
Therefore, it is an object of the present invention to provide a method of high accuracy and robustness which allows the characterization of individual particles based on their fluorescence properties.
According to the present invention, a method for characterizing samples having fluorescent particles is presented which comprises the following steps. At first particles in a measurement volume are excited by a series of excitation pulses and the emitted fluorescence is monitored by detecting sequences of photon counts. For this purpose, a confocal epi-illuminated microscope might preferably be used in connection with a high repetition rate (e.g. 100 MHz) laser pulse excitation. Numbers of photon counts in counting time intervals of given width are determined as well as the detection delay times of the photon counts relative to the corresponding excitation pulses. A function of said detection delay times is builtxe2x80x94as described in detail belowxe2x80x94and as a next step a probablity function of at least two arguments, {circumflex over (P)}(n, t, . . . ) is determined, wherein at least one argument is the number of photon counts and another argument is said function of detection delay times. Thereafter, a distribution of particles as a function of at least two arguments is determined on basis of said probability function {circumflex over (P)}(n, t, . . . ), wherein one argument is a specific brightness (or a measure thereof) of the particles and another argument is a fluorescence lifetime (or a measure thereof) of the particles. The method according to the present invention, called Fluorescence Intensity and Lifetime Distribution Analysis (FILDA) has the advantage that it is possible to determine absolute concentrations, a quantity that is not directly accessible with conventional FLA. The combined information, when used in such a correlated manner according to the present invention, results in significantly increased accuracy as compared to FIDA and fluorescence lifetime analysis alone. In contrast to BIFL, that searches for fluorescence bursts from single molecules above a certain threshold intensity, FILDA analyses preferably the relative fluctuations of the whole data stream and thus accounts for the possibility of simultaneous photon emission from different molecules. Therefore, the present invention can also be used at significantly higher concentrations than BIFL.
In the following, the underlying theory as well as preferred embodiments are elaborated and applied to simulated as well as experimental data. The outstanding power in resolving different species is shown by quantifying the binding of calmodulin to a peptid ligand, promising a broad applicability in the life sciences.
As outlined above, the present invention relies on a method which is at least two-dimensional: different fluorescent particle species in the sample are distinguished from each other by specific brightness as well as lifetime values. In some cases it might however be advantageous to take into consideration further particle properties, such as their diffusion coefficient or brightness in respect to two different photon detectors monitoring fluorescence of different colour or polarization. In these cases, the method of the present invention is of a higher dimension than merely two-dimensional, which is denoted by the dots in the formula of the probability function. However, for the sake of simplicity most of the following explanations will be elaborated on a two-dimensional case.
According to the present invention, a method has been developed that is suited to discriminate different species of a sample according to their lifetimes, xcfx84, and brightness values, q, as well as to determine their absolute concentrations, c. The key is to analyze a measured two-dimensional FILDA distribution {circumflex over (P)}(n,t)of the number of detected photon counts n and the integrated delay time t, applying a theoretical expression of the expected distribution P(n,t). In the following, an extension of the theory of FIDA (Kask et al., Proc. Natl. Acad. Sci. USA 96, 13756-13761, 1999) will be presented that results in a fast and efficient algorithm capable to fit the measured two-dimensional FILDA distribution. Using the representation of the generating functions, the problem is at first reduced to that of single species. In the case of single species, P(n,t) is expressed as a product of two factors, P(n), which is the photon count number distribution, and P(t|n), which is the integrated delay time distribution over n photon counts. Since the calculation of P(n) is solved by the theory of FIDA and that of P(t|n=1)=P(t) by the theory of FLA, one additionally only needs to calculate P(t|n) from P(t|1).
A major preferred constituent part of the FILDA theory according to the present invention is the concept of generating functions. The generating function of the probability distribution P(n,t) is defined as                               G          ⁡                      (                          ξ              ,              η                        )                          =                              ∑                          n              =              0                        ∞                    ⁢                                    ∑                              i                =                0                            ∞                        ⁢                                          P                ⁡                                  (                                      n                    ,                    t                                    )                                            ⁢                              ξ                                  j                  ⁢                                      xe2x80x83                                    ⁢                  i                                            ⁢                                                η                  j                                .                                                                        (        1        )            
The detection delay time, t, of each photon is represented in discrete intervals. In this definition, it is convenient to select arguments of the generating function, "xgr" and xcex7, in the form eixcfx86. Because of this selection G("xgr",xcex7) and P(n,t) are interrelated by a two-dimensional Fourier transform which can be calculated by fast algorithms (Brigham, The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, N.J., 1974).
The reason why the representation of the generating function is convenient becomes clear when comparing how different contributions are included in P(n,t) and G("xgr",xcex7). For example, if one has two independent fluorescent species which would separately yield distributions P1(n,t) and P2(n,t), then the resulting distribution is expressed as a convolution                                           P            ⁡                          (                              n                ,                t                            )                                =                                    ∑                              u                =                0                            n                        ⁢                                          ∑                                  n                  =                  0                                j                            ⁢                                                                    P                    1                                    ⁡                                      (                                          u                      ,                      v                                        )                                                  ⁢                                                      P                    2                                    ⁡                                      (                                                                  n                        -                        u                                            ,                                              t                        -                        v                                                              )                                                                                      ,                            (        2        )            
while in the representation of the generating function, the relation is expressed as a simple product
xe2x80x83G("xgr",xcex7)=G1("xgr",xcex7)G2("xgr",xcex7).xe2x80x83xe2x80x83(3)
The calculation of convolutions is very time-consuming but the calculation of a product is fast and easy. Furthermore, the generalization of Eq. 3 to more than two species is straightforward. The knowledge of a theoretical description of a single species is already sufficient, because Eq. 3 simply expands this description by a product to the case of several components. Therefore, in the following the case of a single species will be considered.
The probability distribution of the detection delay time of each photon may be considered as a function which is characteristic for the given species, depending neither on the number of photons emitted or detected previously nor on the coordinates of the molecule emitting the photon. This means that P(n,t) can be presented as
P(n,t)=P(n)P(t|n),xe2x80x83xe2x80x83(4)
where P(t|n) is the probability distribution of the integrated detection delay time of n photons and P(n) is the probability distribution to detect n photons within the given counting time interval. Since P(t|n) is calculated from P(t|1) by the n-fold convolution, it can be deduced from Eq. 3 that the one-dimensional generating function of P(t|n) is the n-th power of the generating function of P(t|1):
G(xcex7|n)=[G(xcex7|1]n.xe2x80x83xe2x80x83(5)
Substitution of Eqs. 4 and 5 into Eq. 1 leads to the following expression,                               G          ⁡                      (                          ξ              ,              η                        )                          =                              ∑            n                    ⁢                                                                      P                  ⁡                                      (                    n                    )                                                  ⁡                                  [                                      G                    ⁡                                          (                                              η                        |                        1                                            )                                                        ]                                            n                        ⁢                          ξ              n                                                          (        6        )                                          xe2x80x83                ⁢                  =                                    G              ⁡                              (                                  ξ                  ⁢                                      xe2x80x83                                    ⁢                                      G                    ⁡                                          (                                              η                        |                        1                                            )                                                                      )                                      .                                              (        7        )            
According to Eq. 6, each column of the G("xgr",xcex7)-matrix, corresponding to a given xcex7 value, is a one-dimensional Fourier transform of the function P(n)[G(xcex7|1)]n, while according to Eq. 7, each element of the G("xgr",xcex7)-matrix can also be expressed as a Fourier image of P(n) at the point "xgr"G(xcex7|1).
G(xcex7|1) is the generating function (here: the one-dimensional Fourier transform) of the expected detection delay time distribution of a photon P(t|1) originating from the particular species. The function P(t|1) is the cyclic convolution of the IRF and an exponential function with a decay time characteristic for the given species.
The issue of how P(n) is calculated has been described by Kask et al. (Proc. Natl. Acad. Sci. USA 96, 13756-13761, 1999; the contents of which are herein incorporated by reference) P(n) is calculated with the help of its generating function which in the case of single species is expressed as
G("xgr")=exp[c∫(e("xgr"xe2x88x921)qTB(r)xe2x88x92xe2x88x921)dV],xe2x80x83xe2x80x83(8)
where B(r) is the spatial brightness function, q is the apparent specific brightness, T is the width of the counting time interval, c is the apparent concentration, and dV is a volume element. The integral on the right side of Eq. 8 can be calculated numerically. The relationship between the spatial brightness and the corresponding volume elements (needed in the calculation of the right side of Eq. 8) is preferably expressed by an empirical formula of three adjustment parameters a1, a2, and a3,                                                         ⅆ              V                                      ⅆ              u                                =                                                    A                0                            ⁡                              (                                  1                  +                                                            a                      1                                        ⁢                    u                                    +                                                            a                      2                                        ⁢                                          u                      2                                                                      )                                      ⁢                          u                              a                3                                                    ,                            (        9        )            
where u=ln[B(0)/B(r)] and A0 is a coefficient used to select the unit of volume. However, the relationship between the spatial brightness B and volume elements dV might also be expressed by a relationship             ⅆ      V              ⅆ      u        =                    A                  0          ⁢          u                    ⁡              (                  1          +                                    a              1                        ⁢            u                    +                                    a              2                        ⁢                          u              2                                      )              .  
The relationship between the true and the apparent concentrations and between the true and apparent specific brightness is presented in the theory of FIMDA (Palo et al., Biophys. J. 79, 2858-2866, 2000: the contents of which are herein incorporated by reference).
In the following, a theory is presented predicting how capp and qapp depend on T. The case of single species is studied and the first and the second factorial cumulants of the distribution corresponding to Eq. 3 are calculated. The factorial cumulants are defined as                                                         K              n                        =                                                            (                                      ∂                                          ∂                      ξ                                                        )                                n                            ⁢                              ln                ⁡                                  (                                      R                    ⁡                                          (                      ξ                      )                                                        )                                                              "RightBracketingBar"                          ξ          =          1                                    (9a)            
yielding:
K1= less than n greater than =cappqappT,xe2x80x83xe2x80x83(9b)
K2= less than n(nxe2x88x921) greater than xe2x88x92 less than n greater than 2=cappqapp2T2,xe2x80x83xe2x80x83(9c)
where normalization coniditions
∫BdV=1,xe2x80x83xe2x80x83(9d)
∫B2dV=1.xe2x80x83xe2x80x83(9e)
have been used. (Note that Eqs. 9b and 9c are in total agreement with Qian and Elson""s formulae (Biophys. J. 57:375-380, 1990).) From Eq. 9b one can conclude that
capp(T)qapp(T)= less than I greater than ,xe2x80x83xe2x80x83(9f)
where [I]=[n]T/T is the mean count rate, which does not depend on the choice of T. One shall proceed by employing the following relationship between the second cumulant of the count number distribution P(n;T) and the autocorrelation function of fluorescence intensity G(t)= less than I(0)I(t) greater than xe2x88x92 less than I greater than 2,                                                         ⟨                              n                ⁡                                  (                                      n                    -                    1                                    )                                            ⟩                        T                    -                                    ⟨              n              ⟩                        T            2                          =                              ∫            0            T                    ⁢                                    ⅆ                              t                1                                      ⁢                                          ∫                u                T                            ⁢                                                ⅆ                                      t                    2                                                  ⁢                                                      G                    ⁡                                          (                                                                        t                          2                                                -                                                  t                          1                                                                    )                                                        .                                                                                        (9g)            
Introducing the notation                                           Γ            ⁡                          (              T              )                                =                                    1                                                                    c                    app                                    ⁡                                      (                    0                    )                                                  ⁢                                                      q                    app                    2                                    ⁡                                      (                    0                    )                                                  ⁢                                  T                  2                                                      ⁢                                          ∫                0                T                            ⁢                                                ⅆ                                      t                    1                                                  ⁢                                                      ∫                    0                    T                                    ⁢                                                            ⅆ                                              t                        2                                                              ⁢                                          G                      ⁡                                              (                                                                              t                            2                                                    -                                                      t                            1                                                                          )                                                                                                                                ,                            (9h)            
one gets from Eqs. 9g and 9c
capp(T)qapp2(T)=capp(0)qapp2(0)xcex93(T).xe2x80x83xe2x80x83(9i)
From Eqs. 9f and 9i one gets                                           c            app                    ⁡                      (            T            )                          =                                                            c                app                            ⁡                              (                0                )                                                    Γ              ⁡                              (                T                )                                              .                                    (9j)            xe2x80x83qapp(T)=qapp(0)xcex93(T),xe2x80x83xe2x80x83(9k)
As the final step of deriving the theoretical expression of the generating function of P(n,t) for single species, Eq. 7 and 8 are combined yielding:
G("xgr",xcex7)=exp[c∫dV(exp{["xgr"G(xcex7|1)xe2x88x921]qB(r)T}xe2x88x921)]xe2x80x83xe2x80x83(10)
Eq. 10 is a compact theoretical expression. The dependence of G("xgr",xcex7) on the fluorescence lifetime is expressed solely by the function G(xcex7|1). However, it may be even more transparent from Eq. 6 than from Eq. 10 that two one-dimensional distributions P(n) and P(t|1) fully determine the result G("xgr",xcex7) for single species. For multiple species, Eqs. 3 and 10 yield                               G          ⁡                      (                          ξ              ,              η                        )                          =                  exp          ⁡                      [                                          ∑                i                            ⁢                                                c                  i                                ⁢                                  ∫                                      ⅆ                                          V                      ⁡                                              (                                                                              exp                            ⁢                                                          {                                                                                                [                                                                                                            ξ                                      ⁢                                                                              xe2x80x83                                                                            ⁢                                                                                                                        G                                          i                                                                                ⁡                                                                                  (                                                                                      η                                            |                                            1                                                                                    )                                                                                                                                                      -                                    1                                                                    ]                                                                ⁢                                                                  q                                  i                                                                ⁢                                                                  B                                  ⁡                                                                      (                                    r                                    )                                                                                                  ⁢                                T                                                            }                                                                                -                          1                                                )                                                                                                                  ]                                              (        11        )            
where the subscript i denotes different species.
Discrete Fourier transform algorithms can be used when calculating generating functions from probability distributions or vice versa. This means the distribution function is artificially considered as a function of cyclic arguments. Therefore, cycle periods should be defined. In the count number dimension, it is convenient to define the period at a value of n where P(n) has dropped to practical zero. In the detection delay time dimension, two different period values should be considered.
When P(t|1) is calculated, the selected period of the cycle should coincide with the period of the laser excitation. Here it is taken into account that the fluorescence decay function need not to be dropped to zero during a pulse period, N1. After P(t|1) is calculated in the period of successive excitation pulses 0 less than txe2x89xa6N1, the function is padded by zeros in the interval N1xe2x89xa6t less than N1, where N1 denotes the value of the cycle period of P(n,t) in t-dimension. A value of N1 is selected where the distribution P(n,t) has dropped to practical zero. Thereafter, Eq. 6 is applied to calculate the Fourier image of P(n,t).
As was explained above, when P(t|1) and its generating function are calculated, the selected period of the probability distribution should naturally coincide with the period of laser excitation. Assuming that the pulse period is divided into N1 detection delay time intervals of width xcex94, the ideal periodized probability distribution corresponding to a xcex4-excitation is expressed in the interval 0 less than txe2x89xa6N1 as                                           P            δ                    ⁡                      (            t            )                          =                                            1              -                              ⅇ                                                      -                    △                                    /                  t                                                                    1              -                              ⅇ                                                      -                                          N                      i                                                        ⁢                                      △                    /                    t                                                                                ⁢                      ⅇ                                          -                i                            ⁢                              xe2x80x83                            ⁢                              △                /                t                                                                        (                  11          ⁢          a                )            
xcfx84 denotes lifetime of fluorescence. The easiest way to calculate the convolution of PS(t) with the time response function R(t) (which is a periodized function as well) is through the Fourier transform:
GP(t|1)(xcex7)=GPS(t)(xcex7)GR(t)(xcex7).xe2x80x83xe2x80x83(11b)
For the sake of precision, P(t|1) can be calculated with a high time resolution. One might e.g. use 8 times higher resolution here, as it was done in experiment 2 described below. After P(t|1) is calculated in the interval 0 less than txe2x89xa6N1, the function is amended by a series of zeros in the interval N1xe2x89xa6t less than N1. Here N1 denotes the value of periodization of P(n,t) in t-dimension.
Weights of Fitting
For simplification one may assume that count numbers in consecutive counting time intervals are independent. This assumption is not strictly correct because molecular coordinates are significantly correlated over a few counting intervals, but it can nevertheless be successfully applied. Under this assumption, the number of events with a given pair (n,t) is binomially distributed around the mean, M P(n,t), where M is the number of counting time intervals per experiment. This yields the following expression for weights, W(n,t), of the least squares problem       χ    2    =                    ∑                  n          ,          t                    ⁢                                    W            ⁡                          (                              n                ,                t                            )                                ⁡                      [                                                            P                  ^                                ⁡                                  (                                      n                    ,                    t                                    )                                            -                              P                ⁡                                  (                                      n                    ,                    t                                    )                                                      ]                          2              =          min      ⁢              :                                          W          ⁡                      (                          n              ,              t                        )                          =                  M                      P            ⁡                          (                              n                ,                t                            )                                                          (        12        )            
where "khgr"2 is the least square parameter, {circumflex over (P)}(n,t) is the measured FILDA histogram, and P(n,t) is the theoretical distribution.
The weights, W(n,t), of Eq. 12 are sufficiently good for fitting but would result in underestimated statistical errors if used for this purpose. Therefore, statistical errors of FILDA have been determined from fitting a series of experimental and simulated data.
Coming back to the invention in more general aspects, it shall be mentioned that the second argument of the probability function is not the mere individual detection delay time of each photon, but rather a function thereof such as an integrated detection delay time over all detected photons in a given counting time interval. Note that a molecule can hardly emit two photons from a single excitation pulse, but in the examples presented below, there are 10,000 excitations pulses per a counting time interval, which explains why one can detect tens of photons from a single molecule during that time. This advantageous choice of the second argument is related to the property of fluorescence that a series of photons detected in a short time interval are likely to be emitted by a single molecule, in particular if the optimal concentration for performing the present method is used which is only slightly below one molecule per measurement volume. In classical lifetime analysis this information is lost. For this reason, the method according to the present invention turns out to be a more accurate method of analysis, even if specific brightness values of two particle species present in the sample happen to be identical.
In a preferred embodiment, said function of detection delay times is invariant in respect of the order of detection delay times of photon counts detected in the same counting time interval. Preferably said function of detection times is a sum or a mean. The detection delay times of each photon, i.e. the detection times of photon counts relative to the corresponding excitation pulses, might be expressed by integer numbers having a known relationship to the detection times. This relationship is in ideal a quasi-linear one. The function of detection delay times might preferably be a sum or a mean of said integer numbers.
In a further preferred embodiment, the distribution function of particles is determined by fitting the experimentally determined probability function {circumflex over (P)}(n, t, . . . ) by a corresponding theoretical probability function P(n, t, . . . ). This theoretical distribution function P(n,t, . . . ) is preferably calculated through its generating function             G              P        (                  n          ,          t          ,                      xe2x80x83                    ...                ⁢                  xe2x80x83                )              ⁡          (              ξ        ,        η        ,        ...            )        =                              ∑                      n            =            0                    ∞                ⁢                  xe2x80x83                ⁢                              ∑                          t              =              0                        ∞                    ⁢                      xe2x80x83                    ⁢                                    ξ              n                        ⁢                          η              t                                          ⁢              xe2x80x83            ...        ⁢          xe2x80x83        ⁢                  P        ⁡                  (                      n            ,            t            ,                          xe2x80x83                        ...                    )                    .      
In the case of a single detector, the experimentally determined probability function is a two-dimensional function, as explained above; thus, it is preferred to determine said distribution function of particles by fitting the experimentally determined probability function {circumflex over (P)}(n,t) by a corresponding theoretical probability function P(n,t). The latter is preferably calculated through its generating function             G              P        ⁡                  (                      n            ,            t                    )                      ⁡          (              ξ        ,        η            )        =            ∑              n        =        0            ∞        ⁢          xe2x80x83        ⁢                  ∑                  i          =          0                ∞            ⁢              xe2x80x83            ⁢                        ξ          n                ⁢                  η          t                ⁢                              P            ⁡                          (                              n                ,                t                            )                                .                    
As far as the present invention is performed by fitting a measured two-dimensional distribution of the number of photon counts (n) and the preferably integrated detection delay time (t), the basic issue is a formula of calculation of the theoretical probability distribution P(n,t). Both arguments of the probability distribution are typical examples of additive variables: for example, if a molecule emits n1 photons with integrated detection delay time t1 and another molecule emits emits n2 photons with integrated detection delay time t2, then they together emit n1+n2 photons with integrated detection delay time t1+t2. In this case, it is appropriate to select a representation of the generating function when expressing the probability distribution of interest, as described above.
It is further preferred to determine a temporal response function of the experimental equipment which is to be considered in the calculation of the theoretical distribution P(n, t, . . . ). The temporal response function can be determined from a separate experiment.
In a further preferred embodiment, a set of different values of said width of counting time intervals is used, said width being another argument of said probability function. In this particular case, the diffusion coefficient (or a measure thereof) of the particles can advantageously be determined. Consequently, it becomes a third argument of said distribution function of particles. This embodiment of the present invention is called Fluorescence Intensity Lifetime Multiple Distribution Analysis (FILMDA).
The counting time intervals might be consecutive in time or they might overlap.
As was mentioned above, it is preferred to select concentrations of particles to be approximately one or less molecules per measurement volume. Experiments if performed at significant lower concentrations than one particle per measurement volume would result in a slow acquisition of meaningful information because most of the data collection time is spent on waiting, i.e. with no particles in the measurement volume. This would be a situation which is especially disliked in high throughput screening experiments.
A single, two or more photon detectors are used as said detection means, preferably being either an avalanche photodiode or a photomultiplier. At least two photon detectors can e.g. be used to monitor fluorescence of different colour or polarization.
The method according to the present invention is particularly suited for performing high throughput screening assays, assay development and diagnostic purposes. However, it can be applied widely in life sciences and related technologies.
According to the present invention, confocal techniques are particularly suited to monitor fluctuating intensity of fluorescence. They may be appliedxe2x80x94as outlined abovexe2x80x94to a wide field of applications, such as biomedicine, etc. The conjugate focal (confocal) technique is based on using a point source of light sharply focused to a diffraction-limited spot on the sample. The emitted light is viewed through a spatial filter (pinhole) that isolates the viewing area to that exactly coincident with the illuminating spot. Thus, the illumination and detection apertures are optically conjugated with each other. Light originating from focal planes other than that of the objective lens is rejected, which effectively provides a very small depth of field. Therefore, in a particular preferred embodiment of the present invention, a confocal microscope is used for monitoring the intensity of fluorescence. In order to achieve a high signal-to-noise-ratio, it is useful to monitor fluorescence using an apparatus that comprises: a radiation source (12) for providing excitation radiation (14), an objective (22) for focussing the excitation radiation (14) into a measurement volume (26), a detector (42) for detecting emission radiation (30) that stems from the measurement volume (26), and an opaque means (44) positioned in the pathway (32) of the emission radiation (30) or excitation radiation (14) for erasing the central part of the emission radiation (30) or excitation radiation (14). It might be particularly preferred to use an optical set-up described in detail in FIG. 6.
Compared to known multi-dimensional fluorescence fluctuation methods, the method according to the present invention is very special since the second stochastic variable of the histogram (or probability function) is preferably the sum or mean of excitation to detection delay times over the number of photons detected in a given counting time interval. If taken alone, this variable has little if any value. It acquires its meaning only when connected with the number of photon counts. A straightforward selection of the two variable when combining brightness and lifetime analysis would be the number of photon counts and each individual excitation to detection delay time; however, the choice of the present invention creates a method of a significantly better accuracy than the straightforward selection. Another reason of the success of this special selection is that the fit function of the histogram (or probability function) can be calculated fast through its Fourier transform, i.e. using the representation of the generating functions.